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Synthese

, Volume 191, Issue 7, pp 1451–1467 | Cite as

On the epistemological analysis of modeling and computational error in the mathematical sciences

  • Nicolas Fillion
  • Robert M. Corless
Article

Abstract

Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science.

Keywords

Rational reconstruction Mathematical modeling Modeling error  Computational error Backward error analysis 

Notes

Acknowledgments

First and foremost, we would like to thank Robert Batterman. We would also like to thank Erik Curiel, Bill Harper, Robert Moir, Chris Pincock, Bryan Roberts, Chris Smeenk, and two anonymous referees for their useful suggestions.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Statistics and Actuarial Sciences, Joseph L. Rotman Institute of PhilosophyUniversity of Western OntarioLondonCanada
  2. 2.Department of Applied Mathematics, Joseph L. Rotman Institute of PhilosophyUniversity of Western OntarioLondonCanada

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